1,720,995 research outputs found
Stima bayesiana non parametrica della funzione di intensità con applicazione alla valutazione della pericolosità sismica di alcune zone sismogenetiche italiane
No full textNota di presentazione della tesi di dottorato
On Bayesian Nonparametric Estimation of Smooth Hazard Rates with a View to Seismic Hazard Assessment
No full textWORKING PAPER R 38-05, DIPARTIMENTO DI SCIENZE SOCIALI, COGNITIVE E QUANTITATIVE, UNIVERSITA' DI MODENA E REGGIO EMILIA, REGGIO EMILIA, ITALY.Nonparametric inference on the hazard rate is an alternative to density estimation for positive variables which naturally deals with right censored observations. It is a classic topic of survival analysis which is here shown to be of interest in the applied context of seismic hazard assessment. This paper puts forth a new Bayesian approach to hazard rate estimation, based on building the prior hazard rate as a convolution mixture of a probability density with a compound Poisson process. The resulting new class of nonparametric priors is studied in view of its use for Bayesian inference: first, conditions are given for the prior to be well defined and to select smooth distributions; then, a procedure is developed to choose the hyperparameters so as to assign a constant expected prior hazard rate, while controlling prior variability; finally, an MCMC approximation of the posterior distribution is found. The proposed algorithm is implemented for the analysis of some Italian seismic event data and a possible adjustment to a well established class of prior hazard rates is discussed in some detail
On Bayesian analysis of the proportional hazards model
No full textThis work deals with Bayesian inference for Cox's proportional hazards model. After a brief introduction to the problem, from a historical perspective, an MCMC solution is suggested, based on a novel Bayesian nonparametric approach to hazard rate estimation. The suggested method, allowing for right censored as well as exact observations, is then applied to the well-known leukemia remission times in Cox's landmark paper
Objective Bayesian comparison of linear regression models
No full textIn this short paper, I consider the variable selection problem in linear regression models and review two objective Bayesian methods for which I have been developing R code. These two methods, namely, fractional Bayes factors and intrinsic priors, are useful when models are to be compared in lack of substantive prior information. In particular, they are useful when many variables are available for selection, and thus exponentially many models are to be compared, so that subjective prior elicitation under each model is virtually impossible. A case of special interest, which ultimately motivates my work on this topic, is when the structure of an acyclic directed graph is to be learned from data; in this case the model space is even larger, because each graph corresponds to a family of linear regression models
Comments on “Robust Bayesian graphical modeling using Dirichlet t-distributions” by Finegold & Drton
No full textDiscussion contribution
Counting the languages we could speak
No full textThe Principles and Parameters (P&P) approach to the study of the human language faculty, stemming from Chomsky’s investigations in the 1980s, is based on the idea that syntactic knowledge is determined by the interaction of at least two sets of abstract entities: a) Principles, i.e., unvarying linguistic universals; b) Parameters, i.e., open choices between binary values innately predefined by Universal Grammar (UG), that must be closed (set) by language learners on the basis of environmental evidence. Parameters are supposed to be finite in number and to form a list of universal options that define the whole space of variation of biologically acquirable human grammars; thus, the apparently enormous amount of language variation seems reducible to the possible combinations of parameter values. This reduction represents one of the major contributions of P&P theories to the biolinguistic framework, in order to explain cultural variation and to provide a reliable model of language acquisition. Furthermore, recent developments suggest that parametric analyses have the potential to renovate the evolutionary and historical study of cognitive domains.Discovering the whole list of UG parameters is a challenging task which is far from completion. A feasible strategy to systematically analyse parameter variation is to adopt heuristic models which reduce the magnitude of grammatical diversity, though preserving its complexity. The analysis of the (ideally) whole list of parameters concerning a single, independent and internally coherent module of the grammar (the nominal domain) proposed by Longobardi and coauthors is a first contribution in this direction that hints at interesting theoretical and historical results. In particular, partial interactions between parameters and their impact on the downsizing of grammatical variation have been explored; a partial interaction occurs when the setting of a certain (set of) parameter(s) induces the setting of a specific value of another parameter. Focusing on a list of 50 parameters, Longobardi and coauthors show that the phenomenon is quite pervasive: 38 out of 50 parameters undergo the effect of at least one other parameter; 28 out of 50 parameters induce an effect on at least one other parameter. As a consequence, the total number of possible languages comes to be considerably reduced. Assessing the amount of this reduction is the goal of this work.Principles and Parameters models have been implemented since the Eighties in order to solve the contrast between the invariance of the universal language faculty and the actual diversification of languages. According to these theories, the whole space of possible grammars would be defined by means of a complete list of universal parameters and the whole cluster of possible combinations among their value: thus, assuming that parameters are binar, and that they form a universal list of indipendent n members, the whole class of possible Grammars would amount to 2 elevated n members. Yet, parameters are not independent: the values of certain parameters can be set only if other specific parameters are set on a certain specific value; this is the well-known phenomenon of implications among parameters. Working on a cluster of parameters within the nominal domain, Guardiano and Longobardi (since 2005) have shown that the phenomenon of implications is more pervasive than expected, and that implications contribute, in fact, to a sensible downsizing of the possible space of grammatical variation. In this paper we suggest one of the possible methods for calculating the average amount of such a downsizing
Bayesian Non-Parametric Estimation of Smooth Hazard Rates for Seismic Hazard Assessment
No full textHazard rate estimation is an alternative to density estimation for positive variables that is of interest when variables are times to event. In particular, it is here shown that hazard rate estimation is useful for seismic hazard assessment. This paper suggests a simple, but flexible, Bayesian method for non-parametric hazard rate estimation, based on building the prior hazard rate as the convolution mixture of a Gaussian kernel with an exponential jump-size compound Poisson process. Conditions are given for a compound Poisson process prior to be well-defined and to select smooth hazard rates, an elicitation procedure is devised to assign a constant prior expected hazard rate while controlling prior variability, and a Markov chain Monte Carlo approximation of the posterior distribution is obtained. Finally, the suggested method is validated in a simulation study, and some Italian seismic event data are analysed. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008.
On the comparison of regression coefficients across multiple logistic models with binary predictors
Full text linkIn many applied contexts, it is of interest to identify the extent to which a given association measure changes its value as different sets of variables are included in the analysis. We consider logistic regression models where the interest is for the effect of a focal binary explanatory variable on a specific response, and a further collection of binary covariates is available. We provide a methodological framework for the joint analysis of the full set of coefficients of the focal variable computed across all the models obtained by adding or removing predictors from the set of covariates. The result is obtained by applying a specific log-hybrid linear expansion of the joint distribution of the variables that implicitly comprises all the regression coefficients of interest. In this way, we obtain a method that allows one to verify, in a flexible way, a wide range of scientific hypotheses involving the comparison of multiple logistic regression coefficients both in nested and in non-nested models. The proposed methodology is illustrated through a test bed example and an empirical application
A Markovian mixture model for Web data
No full textIn this paper we carry out a site-centric clickstream analysis by fitting a probabilistic model to the click sequences of surfers browsing an e-commerce Web site. In particular, surfers’ paths are modeled as observations originating from a finite mixture of Markov chains which takes values in the site’s page-space. We preliminarily tackle the problem of making inference on the number of distinct visits in which each surfers’ sequence of clicks can be divided. We then deal with goodness-of-fit testing of the model to real data, exploring the heterogeneity of surfers. Finally, by using a simple model with only two components, we shed light on the relationship between surfing behavior and tendency to on-line purchasing
A Comparison of Objective Bayes Factors for Variable Selection in Linear Regression Models
No full textThis paper deals with the variable selection problem in linear regression models and its solution by means of Bayes factors. If substantive prior information is lacking or impractical to elicit, which is often the case in applications, objective Bayes factors come into play. These can be obtained by means of different methods, featuring Zellner-Siow priors, fractional Bayes factors and intrinsic priors. The paper reviews such methods and investigates their finite-sample ability to identify the simplest model supported by the data, introducing the notion of full discrimination power. The results obtained are relevant to structural learning of Gaussian DAG models, where large spaces of sets of recursive linear regressions are to be explored
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